The present invention generally relates to fiber optic gyroscopes. In particular, the present invention relates to a fiber optic gyroscope incorporating a pair of thermally and mechanically symmetrical polarization-maintaining (PM) fiber segments for reducing polarization errors.
Fiber optic gyroscopes (FOG) are increasingly employed in inertial guidance systems due to their ruggedness, compactness, and ability to sense very small rotations in contexts where external navigational cues are unavailable or impracticable in its most basic form. A fiber optic gyroscope system comprises, a xe2x80x9cminimum reciprocal configurationxe2x80x9d as shown in FIG. 1.
Briefly, a light source 11 is used in conjunction with a fiber optic coupler 12, an integrated optic chip (IOC) 16, a loop 10, a photodetector 14, an amplifier 21, a phase sensitive detector (PSD) 23, a bias modulation system 20, and a rotation indicator 26. IOC 16 typically incorporates a polarizer 15, a splitter combiner 17, and a phase modulator 19. Alternatively, individual components, such as a polarizer, coupler and optical phase modulator may be used in the place of IOC 16.
The optical portion of the system contains several features within the optical path to assure that the system is reciprocal, i.e., that substantially identical optical paths are traversed by each of the opposite-traveling electromagnetic waves, except for the specific introductions of non-reciprocal phase difference shifts, as will be described below. Loop 10 comprises a long segment of optical fiber coiled about the rotational axis which is to be sensed. The optical fiber is typically 50 meters to 2,000 meters in length, and is part of a closed optical path in which an electromagnetic wave or light wave, is introduced and split into a pair of waves which propagate in clockwise (cw) and counterclockwise (ccw) directions through loop 10, such that portions of both waves are ultimately diverted by coupler 12 onto a photodetector 14.
The coiled optical fiber which forms loop 10 may be single mode (SM) fiber, a polarization-maintaining (PM) fiber, or a combination of SM and PM fiber. SM fiber allows the paths of the electromagnetic or light waves to be defined uniquely, and further allows the phase fronts of such a guided wave to also be defined uniquely. In contrast, PM fiber is constructed such that a very significant birefringence is produced in the fiber. As a result, polarization fluctuations introduced by unavoidable mechanical stresses, by the Faraday Effect in magnetic fields, or from other sources, which could lead to varying phase difference shifts between the counter-propagating waves, become relatively insignificant.
Thus, either the high refractive index axis, i.e., the slower propagation axis, or the low index axis, is chosen for propagating the electromagnetic waves depending on the other optical components in the system.
The electromagnetic waves which propagate in opposite directions through loop 10 are provided by light source 11. This source is typically a broadband light source, for example, a semiconductor super-luminescent diode or a rare-earth doped fiber light source providing electromagnetic waves, typically in the near-infrared part of the spectrum, over a range of wavelengths between about 830 nm to 1550 nm. Source 11 preferably exhibits a short coherence length for emitted light in order to reduce the phase shift difference errors between these waves due to Rayleigh and Fresnel scattering at scattering sites in loop 10. The broadband source also helps to reduce errors caused by the propagation of light in the wrong state of polarization.
Between light source 11 and fiber optic loop 10 there is shown an optical path arrangement formed by the extension of the ends of the optical fiber forming loop 10 to some optical coupling components which separate the overall optical path into several optical path portions. A portion of optical fiber extends from light source 11 to optical coupler 12 also known as a wave combiner/splitter.
Optical directional coupler 12 has light transmission media therein which extends between four ports, two on each end of the media, which are shown on each end of coupler 12. One of these ports receives the optical fiber extending from light source 11. Another port on the sense end of coupler 12 communicates with photodetector 14, which detects electromagnetic waves, or light waves, impinging thereon, such as through the use of a p-i-n diode. In the case of two nearly coherent light waves, this output generally depends on the cosine of the phase difference between such a pair of substantially coherent light waves.
Optical directional coupler 12 has another optical fiber coupled to a port at the other end thereof which extends to a polarizer 15 provided within IOC 16. The other port on the same side of coupler 12 typically comprises a non-reflective termination arrangement. Optical directional coupler 12, upon receiving a light beam at any of its ports, transmits approximately half of the incoming light to each port on the other end of coupler 12. Conversely, little or no light is transmitted to the port which is on the same end of coupler 12.
In an SM fiber, light can propagate in two polarization modes. Thus, polarizer 15 within IOC 16 is provided for the purpose of passing light propagating at one polarization state such that clockwise (cw) and counterclockwise (ccw) waves of the same polarization are introduced into loop 10, and only light of the same polarization for the cw and ccw waves interfere at detector 14.
Because polarizer 15 does not entirely block the light having an undesirable state of polarization, a small non-reciprocity between the counter-rotating light beams is introduced, causing a non-reciprocal phase shift difference which can vary according to, inter-alia, the environmental conditions. In this regard, the high birefringence in the optical fiber used or the broad bandwidth of the light source used again aids in reducing this resulting phase difference.
Light from polarizer 15 is split by a splitter/combiner 17 provided within IOC 16 such that half of the incoming signal is diverted to one end of loop 10, and half is diverted to the other end of loop 10. The counter-propagating beams returning to IOC 16 are then combined by splitter/combiner 17 and sent to photodetector 14 through polarizer 15 and coupler 12.
Optical modulator 19 provided within IOC 16 is capable of receiving electrical signals and thereby introducing a phase difference in electromagnetic waves transmitted therethrough by either changing the index of refraction or the physical length of the transmission medium, thereby changing the optical path length. Such electrical signals are typically supplied to modulator 19 by the bias modulation signal generator 20 providing either: (1) a sinusoidal voltage output signal at a modulation frequency fb that is intended to be equal to C1 sin(xcfx89bt), where xcfx89b is the radian frequency equivalent of the modulation frequency fb, and C1 is the amplitude of the modulation; or (2) a square wave modulation signal at fb. Other suitable periodic waveforms may also be used.
In general, operation of a fiber optic gyroscope is based on the Sagnac Effect, which describes the behavior of two beams of light traveling in opposite directions around a path undergoing rotation. Of the two light beams, the beam moving in the same direction as the loop""s rotation will necessarily travel a greater distance than the beam traveling the opposite direction. This difference in path length, while small, will necessarily induce a phase shift in the combined beam. The portion of the resultant beam diverted to photodetector 14 through coupler 12 may be analyzed to yield a precise rotation rate. More particularly, the phase shift induced by rotation of the fiber loop is given by:   Δφ  =                    2        ⁢        π        ⁢                  xe2x80x83                ⁢        LD                    λ        ⁢                  xe2x80x83                ⁢        c              ⁢    Ω  
where xcex94xcfx86 is the relative phase shift, L is the fiber length, D is the loop diameter, xcex is the light source wavelength in a vacuum, xcexa9 is the rotation rate, and c is the speed of light in a vacuum. In this way, the system may detect rotation rates to a high degree of accuracy.
The output light intensity impinging on photodetector 14 and hence, the current emanating from the photodetector system photodiode (not shown) in response to the counter-rotating beams, follows a raised cosine function. That is, the output current depends on the cosine of the phase difference between these two waves.
Since a cosine function is an even function, such an output function gives no indication as to the relative directions of the phase difference shift. Consequently, the output function itself provides no indication as to the direction of the rotation about the loop axis. In addition, the rate of change of a cosine function near zero phase is very small, and so such an output function provides very low sensitivity for low rotation rates.
As indicated above, photodetector 14 provides an output photocurrent i, which is proportional to the intensity of the electromagnetic waves impinging thereon, and is therefore expected to follow the cosine of the phase difference between these two waves impinging on that diode.
For sinusoidal bias modulation, the photodiode signal is given by the following equation:
i=(Io/2)xcex7(1+cos(xcfx86R+xcfx86b cos xcfx89bt))
where: Io is the light intensity magnitude at photodetector 14 in the absence of any phase difference between counterclockwise waves and xcex7 is the detector responsivity coefficient.
Thus, the current depends on the resulting optical intensity of the two substantially coherent waves incident on the photodiode provided within photodetector 14, an intensity which will vary from a peak value of Io to a smaller value depending on how much constructive or destructive interference occurs between the two waves. This interference of waves will change with rotation of the coiled optical fiber forming loop 10 about its axis as such rotation introduces a phase difference shift of xcfx86R between the waves. Further, there is an additional variable phase shift introduced in this photodiode output current by modulator 19 with an amplitude value of xcfx86b and which is intended to vary as cos(xcfx89bt), and xcfx89b is the radian frequency equivalent of the modualtion frequency fb supplied by the bias modulation system 20.
Thus, the output signal from photodetection system 14 is converted to a voltage and provided through an amplifier 21 where it is amplified and passed to PSD 23. Photodetection system 14, amplifier 21, PSD 23, and any filters included therein constitute signal component selector 35. PSD 23, serving as part of a phase demodulation system, is a well known device. PSD 23 extracts the amplitude of the fundamental frequency fb of the photodiode provided within photodetector 14 output signal, or the fundamental frequency of modulation signal generator 20 plus higher odd harmonics, to provide an indication of the relative phase of the electromagnetic waves impinging on the photodiode. For additional details regarding phase signal detectors and modulation techniques, see U.S. Pat. No. 5,602,642 to Bergh, et al, which is hereby incorporated by reference.
One challenge that arises in the design of fiber optic gyroscopes is the presence of polarization errors. There are two major classes of polarization errors, amplitude-type polarization errors and intensity-type polarization errors. Amplitude-type polarization errors are those errors that occur where electromagnetic waves that have passed through the blocking axis of polarizer 15, because of polarizer imperfections, coherently mix in any of the loop optical components, such as through splitter 17 and loop 10, with waves that have passed along the transmission axis of polarizer 15.
Intensity-type phase errors occur when electromagnetic wave polarization components that have passed along the transmission axis of polarizer 15 are coupled in any of these same optical components to the polarization components which have passed along the blocking axis and thereafter reach the blocking axis of polarizer 15 to interfere with opposite-traveling waves having the same history. In addition, a phase shift error in the opposite direction occurs for waves passing along the blocking axis of polarizer 15 and being coupled to reach the transmission axis.
Known systems often reduce these unwanted phase shift error via the use of one or more depolarizers. More particularly, referring now to FIG. 2, two segments of PM fiber 40(a) and 40(b) are spliced into the SM fiber comprising loop 10 via splices 52 and 53. These polarizers lead to the relatively uniform mixing of the electromagnetic wave components from the transmission and blocking axes of polarizer 15. To avoid signal fading, the depolarizers used on the ends of the SM fiber loop are typically of different lengths.
Depolarizers 40(a) and 40(b) distribute portions of the incoming wave components into orthogonal polarization states such that they become mixed at the other end of the depolarizer.
Referring now to FIG. 3, a birefringent fiber 40A is suitably designed to exhibit a difference in refractive index between orthogonal axes x and y, namely NX and NY, respectively. Birefringence may be induced through the use of an elliptical core or by imbedding stress rods within birefringent fiber 40A, as shown in FIG. 3. A pulse of light 304 entering the fiber at a 45-degree angle, such as via a 45-degree splice, is split into two components: Ax 308 along the fast axis and Ay 306 along the slow axis, separated by a delay of xcex94Lopt. The use of depolarizers 40A results in a significant cost savings as it obviates the need for using expensive PM fibers 40(a) and 40(b) for loop 10.
While it is possible to reduce polarization errors through the use of one or more polarizers as shown in FIG. 2, this configuration has a number of drawbacks. For example, the resultant system is susceptible to errors arising due to thermal excursions, such as rapid increases or decreases in temperature. This type of error is sometimes referred to as xe2x80x9cT-dotxe2x80x9d error, wherein the dot denotes the time rate of change of T. The errors xcex94xcfx86 resulting from fiber characteristics and the presence of different types of depolarizers 40 inserted into an otherwise optical loop is given by:   Δφ  =                    ⅆ        OPL                    ⅆ        T              ⁢                  ⅆ        T                    ⅆ        t              ⁢    Δ    ⁢          xe2x80x83        ⁢    t  
where: xcex94t is the time difference between when the two counter propagating waves pass through the point of interest, t is time, T is temperature, and OPL is optical path length. The further a point is from the center of the optical loop, the larger the time differential xcex94t, and therefor the larger the sensitivity. This implies that the depolarizers, located between the IOC and the loop, are the most sensitive sections of the optical loop.
Great care is often taken to wind loop 10 such that antipodal points on the loop are located proximate each other. In this way, any temperature variations experienced by a portion of the loop result in thermal expansions and/or contractions which tend to cancel each other out. With depolarizers 40 in the loop, however, there will be points along SM loop 10 which are adjacent to PM fibers 40(a) and 40(b). As SM fiber and PM fiber have very different structures in terms of core dimensions, cladding, buffers, etc., the two adjacent sections of fibers will generally react differently to thermal stress. That is, one type of fiber will generally expand or contract relative to the other fiber, resulting in a small but significant difference in path lengths between counter-rotating light beams.
Additional background information regarding polarization errors can be found in the proceedings reprint by Szafraniec et al., entitled xe2x80x9cPerformance Improvements in Depolarized Fiber Gyrosxe2x80x9d which was presented at the EUROPT Conference on Fiber Optic and Laser Sensors XIII, in Munich, Germany, Jun. 20-21, 1995, and U.S. Pat. No. 5,377,283 to Blake, et al., which are both hereby incorporated by reference.
In light of the above, systems and methods are needed in order to overcome these and other limitations of the prior art. Specifically, there is a long-felt need for precise fiber optic gyroscopes which minimize polarization errors while maintaining mechanical and thermal symmetry of the fiber loop.
In accordance with an aspect of the present invention, a fiber optic gyroscope comprises a loop, a depolarizing region, first, second, third, and fourth optical sections, and first, second, third and fourth splices. The loop includes a single mode optical fiber having a first end and a second end. The depolarizer region is coupled to the loop, and the depolarizer region includes the first optical fiber section coupled to the second optical fiber section via the first splice, and the third optical fiber section is coupled to the fourth optical fiber section via the third splice. The first optical fiber section is coupled to the first end of the loop via a second splice, and the third fiber section is coupled to the second end of the loop via a fourth splice. The first, second, third, and fourth fiber sections comprise polarization maintaining fibers. The first splice has an alignment between 35xc2x0 and 55xc2x0 between a major axis of polarization of the first optical fiber section and a major axis of polarization of the second optical fiber section, and the third splice has an alignment between 35xc2x0 and 55xc2x0 between a major axis of polarization of the third fiber section and a major axis of polarization of the fourth fiber section. As a result, thermal and mechanical influences on the optical path lengths of each one of the optical fiber sections are substantially the same.
In another aspect of the present invention, a method for minimizing time-derivative errors in a fiber optic gyroscope comprises the following: providing a depolarizer having two segments of polarization maintaining optical fiber coupled to an optical fiber loop wherein the two segments are of substantially equal length; providing each polarization maintaining optical fiber segment with two optical fiber sections connected together via a splice, each splice having an angle from about 35xc2x0 to 55xc2x0 between major axes of polarization of the corrsponding pair of optical fiber sections; and choosing the length of each optical fiber section to maintain thermal and/or mechanical symmetry of the optical fiber loop.
In accordance with a further aspect of the invention, an inertial guidance system includes a fiber optic gyroscope. The fiber optic gyroscope comprises a light source having a short coherence length, an integrated optic chip coupled to the light source, a fiber loop having a fixed length, and a depolarizer. The depolarizer includes two polarization maintaining fiber segments. Each of the fiber segments includes one or more splices and couples a respective end of the fiber loop to the integrated optic chip, so that mechanical and/or thermal symmetry is maintained and polarization errors are suppressed.